There are hosted CI solutions that can orchestrate locally installed agents. The two that come to mind are Microsoft’s Visusl Studio Team Services and AWS Code Deploy.
For both, you install a local agent that polls the website for commands. You can manually kick off a “deployment” that just downloads and run scripts. Both have agents for Windows and Linux.
VSTS is free for private environments for five users and like $5 a month for additional users for one simultaneously running agent - you can have as many agents as you want installed but only one will deploy at a time. Additional simultaneously running agents are cheap or free for each registered MSDN subscriber who is a user.
AWS Code Deploy is similar. It’s free for AWS hosted EC2 instances and a 1 cent for each on prem deployment.
They both support the concept of deployment groups where you can run the same deployments on a group of machines.
Code Deploy uses a simple YML file that tells Code Deploy which scripts/batch files to run.
They both support integration with GitHub via webhooks.